Research on Magnetic Suspension Control Scheme Based on Feedback Linearization under Low Track Stiffness
Round 1
Reviewer 1 Report
1) In Eq.3, authors did not consider the inductance of coil. Could authors explain the reason?
2) In Eq.1, authors considered external disturbance force fd. Why did authors remove it from Eqs. 7 and 15?
3) There is not $q_i(x)$ in Eq.9. Please check it.
4) Why did author assume F as Eqs.16 and 19? Could authors explain them from the perspective of physical significance?
5) Authors substituted Eq.24 into Eq.20. Was it right? Also, please check "substituting Eq.27 and 28 into Eq.26, yields Eq.25"(Line 290~291), and Line 331.
6) In Fig. 10, how to measure B? Please explain.
7) Authors employed acceleration sensor in the experiment. How did authors to deal with the noise of sensor?
8) The font size was too small in Figs. 12~14.
9) In Figs. 12 and 13, there were delay between B and B-exp. Could authors explain it in detail?
10) There were many peaks in Figs. 12~14. Some were not small. Could authors analyze them in detail?
11) Please cite more current references.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The topic covered in this paper is an occasional problem with EMS magnetic levitation trains. If possible, it would be beneficial for the reader to introduce the vibration problem between the vehicle and the guideway that the authors encountered directly.
The subject of this paper is key to the commercialization of electromagnetic
levitation trains, and is an important subject in the field of magnetic levitation trains. To help readers understand and emphasize the effectiveness of the proposed method, it would be good to add the following two contents.
1. Provide real-world data for "self-excited vibration"
Presenting a real example of "self-excited vibration" occurring on the EMS-type magnetic levitation train will help readers understand the subject of the paper. In other words, it would be better to provide the measured vertical acceleration and airgap history when "self-excited vibration" occurs in a flexible guideway.
2. Presentation of frequency domain analysis results
In this paper, only time domain data from experimental devices are presented for the validity of the proposed method. In order to evaluate the stability of the levitation controller, frequency domain analysis such as Bode diagram is required. It would be desirable to present the result of evaluating the controller performance in the frequency domain.
Author Response
Comment 1： Provide real-world data for "self-excited vibration"
Presenting a real example of "self-excited vibration" occurring on the EMS-type magnetic levitation train will help readers understand the subject of the paper. In other words, it would be better to provide the measured vertical acceleration and airgap history when "self-excited vibration" occurs in a flexible guideway.
Thanks for your suggestion, we have added a picture of the self-oscillation appearing in the experimental section.
Response：We appreciate it very much for this good suggestion, and we have done it according to your ideas. The picture of self-excited vibration has been added as Fig. 13.
Comment 2： Presentation of frequency domain analysis results
In this paper, only time domain data from experimental devices are presented for the validity of the proposed method. In order to evaluate the stability of the levitation controller, frequency domain analysis such as Bode diagram is required. It would be desirable to present the result of evaluating the controller performance in the frequency domain.
Response: Thank you very much for your suggestion, and we have refined the manuscript and the Bode diagram of the system is shown in Fig. 14, and the frequency domain analysis is given in line 447.
Reviewer 3 Report
This paper deals with the problem of vehicle-guideway coupled self-excited vibration in maglev train systems. In this paper, an electromagnetic force model based on least squares fitting is proposed. A control scheme based on the feedback linearization theory is also designed to achieve a stable suspension with low track stiffness. The following comments can be useful to improve the quality of the manuscript.
1) More accurate electromagnetic force model is established based on the least squares fitting method. It is recommended to describe important differences of the proposed electromagnetic force model with respect to other analytical models for electromagnetic forces proposed by other scientific research groups.
2) Since the introduced electromagnetic force model is based on least squares fitting method, explain the possible practical limitations to use in maglev train systems control.
3) A schematic diagram of the nonlinear dynamic systems under study is recommended, where all variables and parameters involved in its modeling is recommended. In Eq. (1) why the gravitational force is positive. Include the reference system in Figure for measurements of system variables.
4) Include more information of external forces f_{d1}.
5) External forces are considered in Eq. (1). Nevertheless, external forces were not considered after in Eqs. (7), (15) …. It would be useful to consider uniformity in all the manuscript.
6) The state space model (28) is used for design of the feedback linearization-based control scheme. Include the effects of external forces.
7) Explain why the control voltage was not considered from the beginning of the control design. The relationship of magnetic flux and the control voltage given by Eq. (45), together Eq. (28) could be considered directly for the control design?
8) A proof of closed-loop stability using the control given by Eq. (50) into the complete nonlinear system model is recommended.
9) The linearization-based control method was used for the design of the proposed control scheme. Nevertheless, there are other control methods which could be used for this application. It thus suggested to explain differences of the proposed control design method with enhanced model reference adaptive control scheme for tracking control of magnetic levitation system; active disturbance rejection control of a magnetic suspension system; nonlinear adaptive control of magnetic levitation system using terminal sliding mode and integral backstepping sliding mode controllers.
10) Include more information of the experimental platform. A picture of the platform is suggested.
11) Quality of several figures of section of experimental verification could be improved to clearly show the results.
12) Provided more information about how the control parameters were selected.
13) Robustness of the proposed control scheme can be much better described by considering self-excited vibration and exogenous resonant vibrations.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 4 Report
attached:
1) the estimations of magnetic force and magnetic flux need enhanced explanations
2) the control scheme needs better explanation
Comments for author File: Comments.pdf
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
None
Reviewer 3 Report
There is no additional suggestion.
